Drake equation

N = R ∗ ⋅ f p ⋅ n e ⋅ f l ⋅ f i ⋅ f c ⋅ L {\displaystyle N=R_{*}\cdot f_{\mathrm {p} }\cdot n_{\mathrm {e} }\cdot f_{\mathrm {l} }\cdot f_{\mathrm {i} }\cdot f_{\mathrm {c} }\cdot L}

This form of the equation first appeared in Drake's 1965 paper.

In September 1959, physicists Giuseppe Cocconi and Philip Morrison published an article in the journal Nature with the provocative title "Searching for Interstellar Communications". Cocconi and Morrison argued that radio telescopes had become sensitive enough to pick up transmissions that might be broadcast into space by civilizations orbiting other stars. Such messages, they suggested, might be transmitted at a wavelength of 21 cm (1,420.4 MHz). This is the wavelength of radio emission by neutral hydrogen, the most common element in the universe, and they reasoned that other intelligences might see this as a logical landmark in the radio spectrum.

Two months later, Harvard University astronomy professor Harlow Shapley speculated on the number of inhabited planets in the universe, saying "The universe has 10 million, million, million suns (10 followed by 18 zeros) similar to our own. One in a million has planets around it. Only one in a million million has the right combination of chemicals, temperature, water, days and nights to support planetary life as we know it. This calculation arrives at the estimated figure of 100 million worlds where life has been forged by evolution."

Seven months after Cocconi and Morrison published their article, Drake began searching for extraterrestrial intelligence in an experiment called Project Ozma. It was the first systematic search for signals from communicative extraterrestrial civilizations. Using the 85 ft (26 m) dish of the National Radio Astronomy Observatory, Green Bank in Green Bank, West Virginia, Drake monitored two nearby Sun-like stars: Epsilon Eridani and Tau Ceti, slowly scanning frequencies close to the 21 cm wavelength for six hours per day from April to July 1960. The project was well designed, inexpensive, and simple by today's standards. It detected no signals.

Soon thereafter, Drake hosted the first search for extraterrestrial intelligence conference on detecting their radio signals. The meeting was held at the Green Bank facility in 1961. The equation that bears Drake's name arose out of his preparations for the meeting.

As I planned the meeting, I realized a few day[s] ahead of time we needed an agenda. And so I wrote down all the things you needed to know to predict how hard it's going to be to detect extraterrestrial life. …

The Drake equation results in a summary of the factors affecting the likelihood that we might detect radio-communication from intelligent extraterrestrial life. The last three parameters, fi, fc, and L, are not known and are very difficult to estimate, with values ranging over many orders of magnitude (see § Criticism). Therefore, the usefulness of the Drake equation is not in the solving, but rather in the contemplation of all the various concepts which scientists must incorporate when considering the question of life elsewhere, and gives the question of life elsewhere a basis for scientific analysis. The equation has helped draw attention to some particular scientific problems related to life in the universe, for example abiogenesis, the development of multi-cellular life, and the development of intelligence itself.

Within the limits of existing human technology, any practical search for distant intelligent life must necessarily be a search for some manifestation of a distant technology. After about 50 years, the Drake equation is still of seminal importance because it is a 'road map' of what we need to learn in order to solve this fundamental existential question. It also formed the backbone of astrobiology as a science; although speculation is entertained to give context, astrobiology concerns itself primarily with hypotheses that fit firmly into existing scientific theories. Some 50 years of SETI have failed to find anything, even though radio telescopes, receiver techniques, and computational abilities have improved significantly since the early 1960s. SETI efforts since 1961 have conclusively ruled out widespread alien emissions near the 21 cm wavelength of the hydrogen frequency.

There is considerable disagreement on the values of these parameters, but the 'educated guesses' used by Drake and his colleagues in 1961 were:

Inserting the above minimum numbers into the equation gives a minimum N of 20 (see: Range of results). Inserting the maximum numbers gives a maximum of 50,000,000. Drake states that given the uncertainties, the original meeting concluded that N ≈ L, and there were probably between 1000 and 100,000,000 planets with civilizations in the Milky Way Galaxy.

This section discusses and attempts to list the best current estimates for the parameters of the Drake equation.

Calculations in 2010, from NASA and the European Space Agency indicate that the rate of star formation in this Galaxy is about 0.68–1.45 solar masses (M☉; 1.35×10–2.88×10 kg) of material per year. To get the number of stars per year, we divide this by the initial mass function (IMF) for stars, where the average new star's mass is about 0.5 M☉. This gives a star formation rate of about 1–3 stars per year.

Analysis of microlensing surveys, in 2012, has found that fp may approach 1—that is, stars are orbited by planets as a rule, rather than the exception; and that there are one or more bound planets per Milky Way star.

In November 2013, astronomers reported, based on Kepler space telescope data, that there could be as many as 40 billion Earth-sized planets orbiting in the habitable zones of Sun-like stars and red dwarf stars within the Milky Way Galaxy. 11 billion of these estimated planets may be orbiting Sun-like stars. Since there are about 100 billion stars in the galaxy, this implies fp · ne is roughly 0.4. The nearest planet in the habitable zone is Proxima Centauri b, which is as close as about 4.2 light-years away.

The consensus at the Green Bank meeting was that ne had a minimum value between 3 and 5. Dutch science journalist Govert Schilling has opined that this is optimistic. Even if planets are in the habitable zone, the number of planets with the right proportion of elements is difficult to estimate. …

As many observers have pointed out, the Drake equation is a very simple model that omits potentially relevant parameters, and many changes and modifications to the equation have been proposed. One line of modification, for example, attempts to account for the uncertainty inherent in many of the terms. Combining the estimates of the original six factors by major researchers via a Monte Carlo procedure leads to a best value for the non-longevity factors of 0.85 per year. This result differs insignificantly from the estimate of unity given both by Drake and the Cyclops report.

Others note that the Drake equation ignores many concepts that might be relevant to the odds of contacting other civilizations. For example, Glen David Brin states: "The Drake equation merely speaks of the number of sites at which ETIs spontaneously arise. The equation says nothing directly about the contact cross-section between an ETIS and contemporary human society". Because it is the contact cross-section that is of interest to the SETI community, many additional factors and modifications of the Drake equation have been proposed.

Robert J. Stern and Taras V. Gerya proposed to add plate tectonics factors in the 2024 paper:

We resolve the Fermi Paradox (1) by adding two additional terms to the Drake Equation: foc (the fraction of habitable exoplanets with significant continents and oceans) and fpt (the fraction of habitable exoplanets with significant continents and oceans that have had plate tectonics operating for at least 0.5 Ga); and (2) by demonstrating that the product of foc and fpt is very small (< 0.00003–0.002). We propose that the lack of evidence for ACCs [active, communicative civilizations] reflects the scarcity of long-lived plate tectonics and/or continents and oceans on exoplanets with primitive life.